The present invention relates to leak detection and more particularly to a method and system for locating leaks in municipal water distribution pipes.
In most municipal water distribution systems a significant percentage of water is lost while in transit from treatment plants to users. According to an inquiry made in 1991 by the International Water Supply Association (IWSA), the amount of lost water is typically in the range of 20 to 30% of production. In the case of some systems, mostly older ones, the percentage of lost water could be as high as 50% or even more. Lost water is usually attributed to several causes including leakage, metering errors, and theftxe2x80x94according to the IWSA survey, leakage is the major cause.
Water leakage is a costly problemxe2x80x94not only in terms of wasting a precious natural resource but also in economic terms. The primary economic loss due to leakage is the cost of raw water, its treatment, and transportation. Leakage inevitably also results in secondary economic loss in the form of damage to the pipe network itself, e.g., erosion of pipe bedding and major pipe breaks, and in the form of damage to foundations of roads and buildings. Besides the environmental and economic losses caused by leakage, leaky pipes create a public health risk as every leak is a potential entry point for contaminants if a pressure drop occurs in the system.
Economic pressure, concern over public health risk and simply the need to conserve water motivate water system operators to implement leak detection surveys. Leaks may in some cases be detected visually by spotting leaking water on the ground surface. In most cases, however, leaks never surface and normally acoustic methods are used to locate leaks by utilizing the sound or vibration induced by water as it escapes from pipes under pressure.
Locating leaks using acoustic equipment normally consist of two phases. In the first phase, an initial survey is conducted by listening for leak sounds using for example listening rods or aquaphones on all accessible contact points with the distribution system such as fire hydrants, valves, etc. Suspect leak locations found in this phase are noted for more accurate determination (pinpointing) in the second phase. Leaks are pinpointed by using geophones or ground microphones to listen for leak sounds on the ground directly above the pipe at very close intervals, e.g., every 1 m (3.3 ft); or by using leak noise correlation devices known as leak correlators.
Listening devices utilize sensitive mechanisms or materials, e.g., piezo-electric elements, for sensing leak-induced sound and vibration. They could be either of the mechanical or electronic type. Modern electronic devices may include signal amplifiers and noise filters, which could be very helpful in adverse environments. The use of listening devices is usually straightforward but their effectiveness depends on the experience of the user.
Locating leaks in water distribution pipes is a classical application of the cross-correlation method described in the book xe2x80x9cEngineering applications of Correlation and Spectral Analysisxe2x80x9d written by J. S. Bendat and A. G. Piersol, and published by John Wylie and Sons, New York, 1980. The method has been applied in U.S. Pat. Nos. 4,083,229 and 5,205,173. In U.S. Pat. No. 5,974,862 several enhancements of the cross-correlation method were applied to improve the method""s accuracy for detecting leaks. The enhancements included achieving higher signal-to-noise ratio by transmitting leak signals using a digital wireless system wherein signals are digitized at the sensor, achieving a higher dynamic range of the measurement system by applying variable-gain to leak signals to utilize the full range of analog-to-digital converters, and introducing an incremental approach in the calculation of the cross-correlation function.
The cross-correlation method works by measuring vibration or sound in the pipe at two points that bracket the location of a suspected leak. Vibration sensors (normally accelerometers) are attached to fire hydrants or any other contact points with water pipes as shown schematically in FIG. 1. Alternatively, hydrophones (or underwater microphones) can be used. These are inserted into fire hydrants using modified hydrant caps. Vibration or sound signals are transmitted from the sensors to the correlator wirelessly or using wires. The cross-correlation is calculated for the measured leak signals directly in the time domain or indirectly in the frequency domain. For leak signals ƒ1(t) and ƒ2(t) in digital form, the estimate of the cross-correlation function (Ĉ12) is calculated in the time domain using the following sum expression:                     C        ^            12        ⁢          (              i        ⁢                  xe2x80x83                ⁢        Δ        ⁢                  xe2x80x83                ⁢        t            )        =            1              N        -        i              ⁢                  ∑                  k          =          1                          N          -          i                    ⁢                        f          1          k                ⁢                  f          2                      k            +            i                              
where i=1, 2, . . . , M, xcex94t is the sampling interval, ƒ1k and ƒ2k are the kth samples of signals 1 and 2, respectively, and N is the total number of digital samples. In the above expression, fewer and fewer terms will be included with increasing i. It is therefore necessary to limit M to a small fraction of N, say {fraction (1/4)}. In the frequency domain, the estimate of the cross-correlation function (Ĉ12) is obtained via the inverse Fourier transform of the cross-spectral function as                     C        ^            12      c        ⁡          (      τ      )        =      Re    ⁡          [                        1          π                ⁢                              ∫            0                                          π                /                Δ                            ⁢                              xe2x80x83                            ⁢              t                                ⁢                                                                      E                  ^                                12                            ⁡                              (                ω                )                                      ⁢                          ⅇ                              j                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                τ                                      ⁢                          ⅆ              ω                                          ]      
where j=xe2x88x921, and Ê12 is estimate of the cross-spectral density function defined as
Ê12(xcfx89)={circumflex over (F)}1*(xcfx89){circumflex over (F)}2(xcfx89)
{circumflex over (F)}1 and {circumflex over (F)}2 are the spectral density functions of signals f1(t) and f2(t), respectively. {circumflex over (F)}1* is the complex conjugate of {circumflex over (F)}1. The spectral density function of a signal f(t) is obtained via the Fourier Transform as             F      ^        ⁢          (      ω      )        =            ∫      0      T        ⁢                  f        ⁢                  (          t          )                    ⁢              ⅇ                              -            j                    ⁢                      xe2x80x83                    ⁢          ω          ⁢                      xe2x80x83                    ⁢          t                    ⁢              ⅆ        t            
For signals in digital form, the integrals in the above equations are evaluated by using equivalent summation expressions.
The cross-correlation function obtained in the frequency domain is circular, as indicated by the superscript c. This is due to the implicit periodicity of the time signals in the Fourier transform of finite signals. Time delays corresponding to peaks of circular correlation functions might be distorted. The circular effect is easily eliminated by padding time signals with a zero-amplitude segment of length T.
The estimate of the cross-spectral density function used in the above equations is usually obtained by averaging the results of calculations performed for several records or measurements of time signals as                     E        ^            12        ⁡          (      ω      )        =            1              N        r              ⁢                  ∑                  k          =          1                          N          r                    ⁢              xe2x80x83            ⁢                                    F            1                          k              *                                ⁡                      (            ω            )                          ⁢                              F            2            k                    ⁡                      (            ω            )                              
where k designates signal or record number and Nr is the total number of measurements. Averaging reduces the effect of incoherent random noise on the accuracy of the cross-correlation function. A measure of the relationship of the response at the two measurement points for a particular frequency components is provided by the coherence function defined as                     γ        ^            12      2        ⁡          (      ω      )        =                    "LeftBracketingBar"                                            E              ^                        12                    ⁡                      (            ω            )                          "RightBracketingBar"            2                                            E            ^                    11                ⁡                  (          ω          )                    ⁢                                    E            ^                    22                ⁡                  (          ω          )                    
where Ê11 and Ê22 are estimates of the auto-spectra of measurements at locations 1 and 2, respectively. The value of {circumflex over (xcex3)}122 ranges from 0 to 1xe2x80x94a value of 1 indicates that signals at location 1 and 2 are caused by the same source(s) and value of 0 indicates that the signals at the two locations are unrelated. Values between 0 and 1 indicate the presence of related and unrelated components.
If a leak exists between the two measurement points, the cross-correlation function will have a distinct peak and the corresponding time shift (xcfx84max) will correspond to the difference in arrival times between measured leak signals. In reference to FIG. 1, the time delay between measured leak signals is related to the location of the leak relative to measurement points by       τ    max    =                    L        2            -              L        1              c  
where L1 and L2 are the positions of the leak relative to sensors 1 and 2, respectively, and c is the propagation velocity of the leak sound in the water pipe. For leaks located at mid-point between the sensors, the time delay is zero. By substituting L2=Dxe2x88x92L1 in the above equation, the position of the leak relative to point 1 is found as       L    1    =            D      -              c        ·                  τ          max                      2  
where D is the distance between the sensorsxe2x80x94usually measured on site or read off system maps. The propagation velocity c depends on the type and size of pipe. Velocity values could be obtained from pipe manufacturers or they could be calculated using the following equation:   c  =            c      o        ⁢                  1                  [                      1            +                                          a                ⁢                                  (                                      D                    /                    e                                    )                                            ⁢                              (                                                      K                    w                                    /                                      E                    p                                                  )                                              ]                    
where co is the propagation velocity of sound in an infinite body of water equal to {square root over (Kw/xcfx81)}, Kw is the bulk modulus of elasticity of water, xcfx81 is density of water, Ep is the modulus of elasticity of the pipe material, D is internal diameter of the pipe, e is the thickness of the pipe wall, and a is constant that depends on the constraints of longitudinal movement of the pipe (a equals 1 for pipes having expansion joints, which is normally the case for water distribution pipes). Preferably, for more accuracy, the propagation velocity should be measured on-site using a known in-bracket or out-of-bracket simulated leak source.
In most cases, leak signals must be filtered to remove high-amplitude narrow-band noise, e.g., resonance response of the pipe and electrical noise caused by ground loops at the power mains frequency. Otherwise, the cross-correlation function of leak signals will be dominated by the frequencies in the narrow-band resonance response or noise and in turn obscures or distorts the peak corresponding to the leak position.
Alternatively, the time difference between leak signals can be determined using the impulse response function also described in the book xe2x80x9cEngineering applications of Correlation and Spectral Analysisxe2x80x9d written by J. S. Bendat and A. G. Piersol, and published by John Wylie and Sons, New York, 1980. The impulse response function was applied in U.S. Pat. No. 5,038,614 for calculating the time shift between leak signals in wellbore conduits and pipes. The impulse response function is defined as the inverse Fourier transform of the frequency response function (i.e., transfer function between output and input), that is,                     I        ^            12      c        ⁡          (      τ      )        =      Re    ⁡          [                        1          π                ⁢                              ∫            0                                          π                /                Δ                            ⁢                              xe2x80x83                            ⁢              t                                ⁢                                                                      H                  ^                                12                            ⁡                              (                ω                )                                      ⁢                          ⅇ                              j                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                τ                                      ⁢                          ⅆ              ω                                          ]      
where the transfer function Ĥ12(xcfx89) is given as                     H        ^            12        ⁢          (      ω      )        =                    E        ^            12                      E        ^            11      
Previous implementations of the cross-correlation and impulse response methods for detecting leaks in municipal water distribution pipes as well a traditional listening devices suffer from several disadvantages. These include the following:
The cross-correlation method does not perform well for leak signals that have concentration of power in a narrow frequency band. For such signals, commonly found in plastic pipes, peaks corresponding to a leak and those caused by out-of-bracket sources become distorted or difficult to distinguish due to the xe2x80x9cspreading effectxe2x80x9d of the peaks. The narrower the frequency band the more spread are the peaks and in the limit the cross-correlation function becomes a harmonic one for infinitely narrow-band signals.
For narrow band signals, the impulse response function might provide improved resolution of cross-correlation peaks due to its xe2x80x9ccomputational whiteningxe2x80x9d effect of leak signals. Although the impulse response method might provide improved resolution for signals having power concentration in one or more frequency bands, the spectrum of the signals must extend over a wide range. In other words, the impulse response function, does not provide improved performance for xe2x80x9ctrulyxe2x80x9d narrow band signals in which the data outside the main frequency band is extremely small and/or is dominated by noise. Leak signals in plastic pipes are truly narrow band signals.
In plastic pipes also, leak signals are attenuated over distance at a much higher rate that in other types of pipe. In view of the fact that the leak is usually positioned asymmetrically between measurement points, measured leak signals will have significantly different power levels. Therefore if the higher level signal is used as the reference one in the impulse response calculation, the whitening effect of this method will not be effective and the transfer function will be dominated very narrow band peaks, e.g., resonance response of the pipe.
Previous implementations of leak detection systems require specially designed and integrated hardware. Therefore, they are expensive, inflexible, and difficult to modify.
Existing listening devices are not effective for leaks in plastic pipes unless they are used very closed to leaks. The power of leak signals in plastic pipes is concentrated in a narrow low-frequency range ( less than 50 Hz). The human hearing is not sensitive enough to sound at frequencies in this range.
Pre-filtering of leak signals using digital filters to remove interfering noise is time consuming. This is especially the case when leak signals have to be analyzed several times to find an optimum cross-correlation result or when very long leak signals have to be used to improve signal-to-noise ratio for low level leak signals.
In order to overcome some of the above noted shortcomings of the prior art it is an object of the invention to provide an improved method of leak detection.
In accordance with the invention there is provided a method of detecting leaks in pipes, in particular plastic pipes and other non-metallic pipes, comprising the steps of: measuring of leak-induced sound or vibration in a water pipe from a first location and from a second location simultaneously to provide first and second signals respectively, the first and second location separated by a known distance of pipe; and, calculating an enhanced impulse response function or a post-filtered cross-correlation function based on the first and second signals to determine a leak location within the pipe, the leak location a distance from the first location. In accordance with the invention also there is provided a method for digitally shifting the frequency content of leak-induced sound. In accordance with the invention acquisition and processing of and listening to leak signals are carried out via multimedia-equipped personal computers. The present invention offers the following advantages:
The enhanced impulse response method eliminates the need for pre-or post-filtering of interfering noises and hence eliminates the uncertainty and difficulties encountered by non-experts in selecting filter settings especially for low-frequency narrow band signals such as those prevalent in plastic and other non-metallic pipes.
Post-filtering of the cross-correlation function using digital filters is considerably more efficient than the prior practice of pre-filtering leak signals.
Digitally shifting the frequency content of leak-induced sound makes it possible to hear low-frequency leak-induced sound prevalent in plastic and other non-metallic pipes by shifting their frequency content to a range audible to a typical human ear.
Utilising multimedia-equipped personal computers to record, process and playback leak signals provides proved suitable for low-level signals and in turn eliminated the need for specialised and costly data acquisition and processing hardware.